The direct observation of high-energy cosmic rays, up to the PeV energy region, will increasingly rely on highly performing calorimeters, and the physics performance will be primarily determined by their geometrical acceptance and energy resolution. Thus, it is extremely important to optimize their geometrical design, granularity and absorption depth, with respect to the totalmass of the apparatus, which is amongst the most important constraints for a space mission. CaloCube is an homogeneous calorimeter whose basic geometry is cubic and isotropic, obtained by filling the cubic volume with small cubic scintillating crystals. In this way it is possible to detect particles arriving from every direction in space, thus maximizing the acceptance. This design summarizes a three-year R&D activity, aiming to both optimize and study the full-scale performance of the calorimeter, in the perspective of a cosmic-ray space mission, and investigate a viable technical design by means of the construction of several sizable prototypes. A large scale prototype, made of a mesh of 5x5x18 CsI(Tl) crystals, has been constructed and tested on high-energy particle beams at CERN SPS accelerator. In this paper we describe the CaloCube design and present the results relative to the response of the large scale prototype to electrons.